Chi2Gehrels
- class sherpa.stats.Chi2Gehrels(name='chi2gehrels')[source] [edit on github]
Bases:
Chi2
Chi Squared with Gehrels variance.
The variance is estimated from the number of counts in each bin, but unlike
Chi2DataVar
, the Gaussian approximation is not used. This makes it more-suitable for use with low-count data.The standard deviation for each bin is calculated using the approximation from 1:
sigma(i,S) = 1 + sqrt(N(i,s) + 0.75)
where the higher-order terms have been dropped. This is accurate to approximately one percent. For data where the background has not been subtracted then the error term is:
sigma(i) = sigma(i,S)
whereas with background subtraction,
sigma(i)^2 = sigma(i,S)^2 + [A(S)/A(B)]^2 sigma(i,B)^2
A(B) is the off-source “area”, which could be the size of the region from which the background is extracted, or the length of a background time segment, or a product of the two, etc.; and A(S) is the on-source “area”. These terms may be defined for a particular type of data: for example, PHA data sets A(B) to
BACKSCAL * EXPOSURE
from the background data set and A(S) toBACKSCAL * EXPOSURE
from the source data set.See also
Notes
The accuracy of the error term when the background has been subtracted has not been determined. A preferable approach to background subtraction is to model the background as well as the source signal.
References
- 1
“Confidence limits for small numbers of events in astrophysical data”, Gehrels, N. 1986, ApJ, vol 303, p. 336-346. http://adsabs.harvard.edu/abs/1986ApJ…303..336G
Methods Summary
calc_chisqr
(data, model)Return the chi-square value for each bin.
calc_stat
(data, model)Return the statistic value for the data and model.
calc_staterror
(data)Return the statistic error values for the data.
goodness_of_fit
(statval, dof)Return the reduced statistic and q value.
Methods Documentation
- calc_chisqr(data, model) [edit on github]
Return the chi-square value for each bin.
- Parameters
data (
sherpa.data.Data
orsherpa.data.DataSimulFit
) – The data set, or sets, to use.model (
sherpa.models.model.Model
orsherpa.models.model.SimulFitModel
) – The model expression, or expressions. If asherpa.models.model.SimulFitModel
is given then it must match the number of data sets in the data parameter.
- Returns
chisqr – The per-bin chi-square values.
- Return type
array of numbers
- calc_stat(data, model) [edit on github]
Return the statistic value for the data and model.
- Parameters
data (
sherpa.data.Data
orsherpa.data.DataSimulFit
) – The data set, or sets, to use.model (
sherpa.models.model.Model
orsherpa.models.model.SimulFitModel
) – The model expression, or expressions. If asherpa.models.model.SimulFitModel
is given then it must match the number of data sets in the data parameter.
- Returns
statval (number) – The value of the statistic.
fvec (array of numbers) – The per-bin “statistic” value.
- static calc_staterror(data)[source] [edit on github]
Return the statistic error values for the data.
- Parameters
data (scalar or 1D array of numbers) – The data values.
- Returns
staterror – The errors for the input data values (matches the data argument).
- Return type
scalar or array of numbers
- goodness_of_fit(statval, dof) [edit on github]
Return the reduced statistic and q value.
The reduced statisitc is conceptually simple, as it is just statistic / degrees-of-freedom, but it is not meaningful for all statistics, and it is only valid if there are any degrees of freedom.
- Parameters
- Returns
rstat (float or NaN or None) – The reduced statistic. If the statistic does not support a goodness of fit then the return value is
None
. If it does then NaN is returned if either the number of degrees of freedom is 0 (or less), or the statistic value is less than 0.qval (float or NaN or None) – The q value. If the statistic does not support a goodness of fit then the return values are
None
. If it does then NaN is returned if either the number of degrees of freedom is 0 (or less), or the statistic value is less than 0.